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If 
p and 
q vary inversely and 
p is 9 when 
q is 5 , determine 
q when 
p is equal to 3 .
Answer:

If p p and q q vary inversely and p p is 99 when q q is 55 , determine q q when p p is equal to 33 .\newlineAnswer:

Full solution

Q. If p p and q q vary inversely and p p is 99 when q q is 55 , determine q q when p p is equal to 33 .\newlineAnswer:
  1. Given relationship and constant: Given that pp and qq vary inversely, we can write the relationship as p=kqp = \frac{k}{q}, where kk is the constant of variation.
  2. Find constant of variation: We know that pp is 99 when qq is 55. We can use these values to find the constant of variation kk. Substitute pp with 99 and qq with 55 into the equation p=kqp = \frac{k}{q}. 9900
  3. Write inverse variation equation: To find kk, multiply both sides of the equation by 55.9×5=k9 \times 5 = k45=k45 = k
  4. Substitute values and solve: Now that we have the constant of variation kk, we can write the inverse variation equation as p=45qp = \frac{45}{q}.
  5. Find value of \newlineqq: We want to find \newlineqq when \newlinepp is equal to \newline33. Substitute \newlinepp with \newline33 into the equation \newlinep=45qp = \frac{45}{q}.\newline\newline3=45q3 = \frac{45}{q}
  6. Find value of q: We want to find q when p is equal to 33. Substitute p with 33 into the equation p=45qp = \frac{45}{q}.\newline3=45q3 = \frac{45}{q}To solve for q, multiply both sides of the equation by q and then divide by 33.\newline3q=453q = 45\newlineq=453q = \frac{45}{3}\newlineq=15q = 15

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